1. Field of the Invention
The present invention relates to a process simulation method and system applicable to semiconductor device fabrication and more particularly, to a topography simulation method and system of a plasma-assisted etching process that employs the well-known Monte Carlo method.
2. Description of the Prior Art
In recent years, to implement higher-level integration of electronic elements on a semiconductor substrate, there has been the increasing need for better profile and dimension control in etching processes to form finer microstructures.
To form microstructures of semiconductor devices with the use of etching techniques, it is important to estimate or predict the post-etching topography of the microstructures through simulation from a standpoint of efficiency improvement in semiconductor device fabrication and development.
Conventionally, various topography simulation methods of etching processes have been popularly used in the semiconductor device fabrication field, which are based on the supposition that the etching process has an isotropy or perfect anisotropy. In these conventional topography simulation methods, however, it has become difficult to precisely represent the actual etching process because of the recent progress in microstructure formation or fabrication. Therefore, these conventional methods have become poor in usefulness.
Thus, there is the need for a novel, useful topography simulation method of etching processes.
On the other hand, analysis for plasma employed in plasma-assisted etching has been made in several ways and the plasma-analyzing techniques have been progressing. For example, a technique to analyze the electric potential distribution and the particle concentration in plasma using the fluid model or the Monte Carlo method have been developed and reported. These conventional plasma-analyzing techniques make it possible to simulate the plasma-assisted etching process and to predict the post-etching topography of the microstructures.
In one of the known calculation methods for simulating the etching topography using the analysis result of plasma, the surface state of minute regions of a target material to be etched is represented by using the type and rate of absorption species existing on the minute regions. In this calculation method, the absorption equilibrium equation, which relates to the chemical equilibrium between the absorption and desorption amounts of the species on the minute regions, is used. Also, in order to calculate the post-etching profile at the next time step, the surface state of the minute regions is renewed at each time step based on the calculation result, thereby changing the profile represented by the string elements and the string points of the "string model".
A conventional topography simulation method using the surface state of minute regions of a target material described above is disclosed in an article entitled "Simulation Approach for Achieving Configuration Independent Poly-silicon Gate Etching", International Electron Devices Meeting (IEDM) Technical Digest, 1995, pp. 105-108, written by K. Harafuji et al., and an article entitled "Modeling and Simulation of Dry-etching", Japan Journal of Applied Physics, Vol. 62, No. 11, 1993, pp. 1111-1117.
In this conventional topography simulation method, the surface state of the minute regions of the target material is represented by the type and rate of the absorption species absorbed onto the minute regions of the target material.
First, the electric potential and particle concentration in a bulk-plasma region of a radio-frequency (RF) glow discharge are analyzed in a bulk-plasma analyzer section.
Second, the trajectory and energy of the incoming particles or species in a sheath-plasma (or, ion transfer) region of the glow discharge are analyzed in a sheath-plasma analyzer section. Using the resultant trajectory and energy of the incoming particles, the flux of the incoming particles is calculated.
Third, in a surface-reaction calculator section, the absorption equilibrium equation between the flux of the incoming particles and the absorbed species existing on the minute surface regions of the target material is solved. Thus, the time-dependent composition change of the absorbed species onto the minute surface regions of the target material, which is caused by the chemical reaction on the surface regions, is calculated.
The time-dependent composition change of the absorbed species thus calculated represents the surface state change of the minute surface regions of the target material.
To simulate the post-etching topography of the target material, it is supposed that the minute surface regions of the target material are etched by chemical reaction between the flux of the incoming particles and the absorbed species onto the minute surface regions of the target material according to the time-dependent composition change of the absorbed species.
Finally, in a topography calculator section, the post-etching topography of the target material is calculated using the time-dependent composition change of the absorbed species while the well-known string model is applied to the minute surface regions of the target material.
With the conventional topography simulation method using the surface state of minute regions of a target material disclosed in the above articles, however, there is a problem that a satisfactory calculation or simulation accuracy is not given. This is because the elemental processes or reactions on the minute surface regions of the target material are not identified and therefore, the simulation is not performed in the particle level. In other words, since the time-dependent composition change of the absorbed species on the minute surface regions of the target material is calculated by solving the absorption equilibrium equation between the absorption and the desorption amounts of the species, the chemical reactions between the individual species or particles are not sufficiently considered. These chemical reactions are replaced with the absorption equilibrium.
Moreover, the conventional topography simulation method disclosed in the above articles has another problem that a long calculation time is necessary. This is because the absorption equilibrium equation needs to be solved with respect to all types of the relating absorption species.
However, the actual chemical reactions will occur due to action of the specific absorption species and therefore, all types of the relating absorption species need not be considered for this purpose.
Additionally, the long-time use of computers increases not only the simulation cost but also the load on the computers. As a result, computer simulation is required to be finished in a time period as short as possible.
To cope with this requirement, the inventor created an improved topography simulation method and reported, which was filed as the Japanese Patent Application No. 7-328640 in 1995.
FIG. 1 schematically shows the improved topography simulation method disclosed in the Japanese Patent Application No. 7-328640.
As shown in FIG. 1, first, in a bulk-plasma analyzer 101, the plasma potential and particle density in a bulk plasma region of a radio-frequency (RF) glow discharge and the sheath length of a sheath plasma region thereof are calculated. The particle density is calculated for ions, electrons, and radicals. Thus, the time-dependent change of the plasma potential, the particle density, and the sheath length is derived.
Second, using the plasma potential and the particle density in the bulk plasma region and the sheath length thus calculated, the type of the incoming particles is selected, and the energy of the selected incoming particle is calculated in a sheath-plasma analyzer 102.
In this procedure, the type of the particles is selected by using a random number and a particle density table. The particle density table includes the particle density for the individual particles such as ions, electrons, and radicals, which is given in the bulk-plasma analyzer 101.
The initial velocity of the selected particle is calculated by using the Monte Carlo method based on the Maxwell distribution. Then, the trajectory of the selected particle is calculated by using the motion equation and the Poisson's equation, thereby deriving the energy of the selected particle.
Third, in a surface reaction calculator 103, the surface reaction occurring on the surface of the target material to be etched is selected in the following way.
The two-dimensional string model is applied to the etch front of the surface of the target material. A minute surface region between the two adjacent string points is selected. The selected particle is collided with this minute surface region.
The surface state of the minute surface region is represented by the type of the particle (i.e., absorption species) and the absorption rate of the particle. The absorption rate of the individual particles is listed in a surface state table.
The type of the absorption species, to which the selected particle in the sheath-plasma analyzer 102 is collided, is selected using the Monte Carlo method.
Next, according to the selected incoming particle and the selected absorption species, a reaction rate is calculated for various possible chemical reactions while considering the energy of the selected incoming particle. The chemical reaction that will occur on the minute surface region due to the selected incoming particle and the selected absorption species is selected using the Monte Carlo method.
Thus, the surface reaction on the minute surface region between the two adjacent string points is calculated. The minute surface region is etched due to the surface reaction, thereby shifting the string points to change the profile of the minute surface region.
The same calculation as the minute surface region is performed for all the string points.
Finally, in a topography data calculator 104, the topography data of the minute surface region is calculated according to the profile change of all the minute surface regions.
Thus, the post-etching topography of the etched surface of the target material is derived.
With the improved topography simulation method disclosed in the Japanese Patent Application No. 7-328640, the type of the incoming particle (i.e., the etching species) is identified or selected by using the Monte Carlo method without solving analytically the absorption equilibrium equation. Accordingly, there is an advantage that the sheath-plasma analysis can be achieved as a whole independent of the possibility or impossibility of analytic solution.
Also, the type and energy of the incoming particle or etching species, the type of the absorbed species to be collided with the incoming particle, and the elementary reaction or reactions that will be caused by the incoming particles and the absorbed species are determined in the respective procedures according to the Monte Carlo method. Thus, there is another advantage that high-speed calculation can be achieved.
As a result, the above-described topography simulation method disclosed in the Japanese Patent Application No. 7-328640 increases the calculation efficiency and analytical accuracy compared with the conventional topography simulation method disclosed in the previously-described articles.
However, the above-described topography simulation method disclosed in the Japanese Patent Application No. 7-328640 has the following disadvantage.
The method disclosed in the Japanese Patent Application No. 7-328640 is effective under the supposition that the absorbed species chemically reacted with the incoming particle is fixed onto the surface of the target material even after the reaction. In other words, no consideration is applied to the phenomenon that the absorbed species onto the surface of the target material will desorb from this surface due to chemical reaction or reactions. This phenomenon is typically caused by the incoming ion or ions during the "ion-assisted etching" process, in which the neighboring atom or atoms of the target material is/are desorbed from its surface due to bombardment with the incoming ion or ions.
Consequently, the topography simulation method disclosed in the Japanese Patent Application No. 7-328640 is unable to be applied to the topography simulation of etching processes of the type where a plurality of particles or atoms affect the etching process.
Additionally, the topography simulation method disclosed in the Japanese Patent Application No. 7-328640 has a possibility that the simulation or calculation accuracy becomes low according to the simulation condition and as a result, this method admits of improvement.